Sr Examen
Ecuación diferencial xy'''=y''-xy'
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Solución
Ha introducido
[src]
3 2
d d d
x*---(y(x)) = - x*--(y(x)) + ---(y(x))
3 dx 2
dx dx
$$x \frac{d^{3}}{d x^{3}} y{\left(x \right)} = - x \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)}$$
x*y''' = -x*y' + y''
Respuesta
[src]
/ | 2\ _ / | 2 \
__2, 1 | 1 0 | x | 3 |_ | 3/2 | -x |
y(x) = C1 + C3*/__ | | --| + C2*x * | | | ----|
\_|2, 4 \3/2, 1/2 0, 0 | 4 / 1 2 \2, 5/2 | 4 /
$$y{\left(x \right)} = C_{1} + C_{2} x^{3} {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{2} \\ 2, \frac{5}{2} \end{matrix}\middle| {- \frac{x^{2}}{4}} \right)} + C_{3} {G_{2, 4}^{2, 1}\left(\begin{matrix} 1 & 0 \\\frac{3}{2}, \frac{1}{2} & 0, 0 \end{matrix} \middle| {\frac{x^{2}}{4}} \right)}$$
Clasificación
nth order reducible